Calculations

Calculations

• Which viewport is the sheet

  Picks the viewport that stands for the sheet itself: at scale 1 and covering every other viewport.

  |s − 1| ≤ 1e-6; covers: |o_x − v_x| + o_w ÷ 2 ≤ v_w ÷ 2 + 1e-6 × max(1, v_w, v_h)

  DWG import: objects from the file's model dwg-import.js

  • CadCraft
  64-bit

• Lineweight in hundredths of a millimeter

  Converts a lineweight in millimeters to the whole number the file stores.

  Math.round(w × 100) for w ≥ 0; negative codes kept

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Spline: fit points or control points

  Decides whether a spline's fit points are written with it, by checking that they still give its control points.

  every |recomputed − stored| ≤ 1e-7 × max(1, max(|x| + |y|))

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Multi-line text anchor and oblique angle

  Moves baseline-anchored text to a top anchor one text height up, and writes the oblique angle as a format code.

  anchor = (x, y) + R(rot) × (0, h); code = \Q followed by degrees to 6 decimals

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Hatch boundary rings

  Writes a hatch's rings as closed polylines, or a 3 or 4 cornered solid fill as a SOLID.

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Hatch pattern lines for the file

  The pattern's line families in drawing units: angle in radians, base point and offset in world axes.

  k = scale ÷ (1 metric, 25.4 otherwise); base = R(turn) × (x, y) × k + origin; offset = (dx cos a − dy sin a, dx sin a + dy cos a)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Dimension points and measurement

  The defining points, text point and measurement written for a dimension.

  measurement = dimMeasure; linear: defPoint = end of the dimension line on the second extension line; radial: near = c + r × (cos a, sin a), far = c − r × (cos a, sin a)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Viewport view height

  The model height a sheet viewport shows, and its view center.

  view height = h ÷ s (s taken as 1 when not above 0)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Sheet paper size and limits

  The paper size in millimeters, the sheet's limits and the sheet viewport's center.

  paper mm = w × 25.4 (inch sheets) or w; limits = (x₀, y₀) to (x₀ + w, y₀ + h); center = (x₀ + w ÷ 2, y₀ + h ÷ 2)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Drawing extents

  The smallest and largest x and y of everything in model space, written to the file's header.

  min and max over the bounds of every object

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Closing point of a ring

  Drops a ring's last point when it repeats the first.

  |first − last| < 1e-12

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Construction line direction

  The unit direction written for an infinite line or ray.

  direction = (dx, dy) ÷ √(dx² + dy²)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• User coordinate system axes

  The origin and the x and y axis vectors of a user coordinate system.

  x axis = (cos θ, sin θ); y axis = (−sin θ, cos θ)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Linetype pattern length

  The total length of one repeat of a linetype's dashes and gaps.

  length = Σ |elementᵢ|

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Transparency to the file's word

  Converts a transparency percentage to the opacity byte the file stores.

  alpha = Math.round(255 × (1 − clamp(tr, 0, 90) ÷ 100)); word = 0x02000000 + alpha

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Opacity byte to transparency

  Converts the file's opacity byte back to a transparency percentage.

  p = Math.round((1 − alpha ÷ 255) × 100); p ≤ 0 → none; capped at 90

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Transparency from a file value

  Reads a transparency word or record: by block, by layer or an opacity byte.

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Dimension lineweight to hundredths

  Converts a dimension line or extension line weight in millimeters to the file's whole number.

  Math.round(v × 100) for v ≥ 0; −1, −2, −3 kept as codes

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Style value to a dimension variable

  Converts one dimension style setting to the value its variable holds in the file.

  real: the number (0 when not finite); int: Math.round; bool: 1 or 0; lineweight: lw100; separator: 44 or 46

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Dimension variable to a style value

  Converts one variable read from a file to the dimension style setting.

  real: parseFloat; int: Math.round(parseFloat); lineweight: x ÷ 100 for 0 ≤ x ≤ 211

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Tolerance mode and text gap

  Works out the tolerance mode (symmetric, deviation, limits, basic) and the text gap from the file's variables.

  symmetric when |tp − tm| < 1e-12; gap < 0 → basic and gap = −gap

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Dimension style as file variables

  Every variable of a dimension style, by name, for a DIMSTYLE record.

  basic tolerance: DIMGAP = −|gap|

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• Hatch pattern origin as text

  Writes a hatch's pattern origin into the file as two numbers in a text field.

  text = CCHORG: followed by x, a comma and y

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

  • CadCraft
  64-bit

• A number from a group value

  Reads one real number from the file's text, or a default when the group is absent.

  value = parseFloat(text)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Arc angles

  An arc's center, radius and start and end angles.

  a = (degrees × π ÷ 180) mod 2π

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Hatch boundary to polygon rings

  Turns a hatch's boundary paths (polylines with bulges, lines and arcs) into rings of points.

  arc edge: steps = max(4, ⌈32 × (a₁ − a₀) ÷ 2π⌉); p = c + r × (cos a, sin a)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Bulge arc to points

  The points along a bulged segment of a hatch boundary polyline.

  θ = 4 × atan(b); r = |c ÷ (2 × sin(θ ÷ 2))|; center = midpoint + normal × r × cos(θ ÷ 2); steps = max(2, ⌈16 × |θ| ÷ π⌉)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Hatch pattern scale, angle and lines

  A pattern hatch's scale, angle and its own pattern lines.

  pattern angle = (degrees × π ÷ 180) mod 2π; dx = o_x cos a + o_y sin a; dy = −o_x sin a + o_y cos a, a = line angle × π ÷ 180

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Block array positions

  The insertion point of each copy of a block placed as a rows-by-columns array.

  p = T(insert) × R(rot) × (c × column spacing, r × row spacing)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Dimension defining points

  The points a dimension measures from, by dimension type.

  linear: p₁ = 13, p₂ = 14, line point = 10, angle = group 50 × π ÷ 180; diameter center = (point 15 + point 10) ÷ 2; four-point angular: vertex from the two lines

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Can the dimension be measured

  Checks that a dimension's points are finite and far enough apart to measure.

  |a − b| > 1e-12

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Viewport scale, center and twist

  A sheet viewport's scale, the model point at its center and its view twist.

  s = viewport height ÷ view height; twist = degrees × π ÷ 180 (or radians from R12 data)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Layer lineweight

  A layer's lineweight in millimeters.

  mm = n ÷ 100 for 0 ≤ n ≤ 211; otherwise default

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Object lineweight and linetype scale

  An object's own lineweight in millimeters and its linetype scale.

  lw = n ÷ 100; linetype scale kept when |s − 1| > 1e-12

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Sheet size from the plot settings

  A sheet's size in its own unit when the layout gives no limits, from the paper size in millimeters.

  size = paper mm ÷ 25.4 (inch sheets) or ÷ 1; width and height swapped when the plot rotation code is odd

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Dimension style numbers

  Brings a dimension style's scale, unit format and decimal places into range.

  scale ≤ 0 → 1; dec, adec, tad, zin → max(0, round(value)); dec ≤ 8

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Construction line direction

  The unit direction of an infinite line or ray.

  direction = (dx, dy) ÷ √(dx² + dy²)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Extra sheet read back from a block

  Rebuilds a sheet and its viewports from the block an R12 file keeps them in.

  viewport center = ((x_min + x_max) ÷ 2, (y_min + y_max) ÷ 2); w = x_max − x_min; h = y_max − y_min

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• A group value by its code

  Turns one group's text into a real number, a whole number, a true or false, or text.

  codes 10–59, 110–149, 210–239, 460–469, 1010–1059: parseFloat; 60–99, 160–179, 270–289, 370–389, 400–409, 420–429, 440–459, 1060–1071: parseInt

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Arc angles

  An arc's start and end angles in radians.

  angle = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Multi-line text direction

  The direction vector of multi-line text, from the file's vector or from its rotation angle.

  x axis = group 11 when present; otherwise (cos(a), sin(a)), a = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Hatch arc and ellipse edges

  The center, radius or axes, and start and end angles of the curved edges of a hatch boundary.

  angle = degrees × (π ÷ 180); missing end angle = 360 degrees

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Number text (R12)

  The text every real number is written as in an R12 file.

  |n| < 1e-12 → 0.0; otherwise n rounded to 15 significant digits

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Point (R12)

  Writes a 2D point as three groups.

  x → f(x); y → f(y); z → 0.0

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Arc (R12)

  An arc's center, radius and its angles in degrees.

  degrees = (a mod 2π) × 180 ÷ π

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Dimension (R12)

  The defining points, text point and angles written for a dimension.

  linear: point 10 = end of the dimension line on the second extension line; radial: near = c + r × (cos a, sin a), far = c − r × (cos a, sin a); angles in degrees

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Viewport view (R12)

  A sheet viewport's twist, view height and view center.

  view height = h ÷ s

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Ellipses and splines as polylines (R12)

  Writes an ellipse or a spline as a polyline along the curve, because R12 has neither object.

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Hatches as solids or outlines (R12)

  Writes a filled triangle or quadrilateral as a SOLID and any other hatch as closed polylines of its rings.

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Text (R12)

  A text's position, height, rotation, width factor and oblique angle.

  rotation° = rot × 180 ÷ π; oblique° = obl × 180 ÷ π

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit